RU-SPB 2012 Problem 111

$a,b,c$ are reals, such that every pair of equations of $x^3-ax^2+b=0,x^3-bx^2+c=0,x^3-cx^2+a=0$ has common root. Prove $a=b=c$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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